How would this graph be classified? And what properties does it have? What would be a natural thing to study with this graph? I know it has 40 nodes. It's undirected. It's planar if I'm not mistaken. Also this graph looks like it's 4-connected except for the 4 outer most nodes.
I read on Wikipedia that: "4-connected planar graphs are always Hamiltonian by a result due to Tutte, and the computational task of finding a Hamiltonian cycle in these graphs can be carried out in linear time." Are 4-connected planar graphs somehow easier to compute Hamiltonian cycles for?
I'm wondering if that result is valid for this graph because 4 nodes have degree 6, while the others have degree 4. Thanks for your help.